If you currently have a template shop, you'll need to recreate your designs for Templett in order for them to be editable by your customers. Unfortunately, there's no way to take a AI or PSD file and convert it to Templett automatically. This may sounds like a daunting task but once you are familiar with the application and the design area, it tends to go pretty fast.
Most sellers start with their most popular designs first and work backwards from there. That way, your top sellers (and the ones probably taking the most of your time with customer service, editing, etc) will be converted first and your workload will start to drop rapidly.
What parts should you make editable?
That is completely up to you and how much control you want to give your customers.
Some sellers upload a jpeg or png that acts as the main design then they add text boxes to the template that are editable. In this case, the main design is not editable but all the text is.
Other sellers want to give their customers full control and the ability to edit everything. These sellers like to upload all their design elements as individual files and add them to the template individually. This allows for more flexibility but it does take longer.
Ultimately, it's up to you which approach you take. If you are thinking long term, it's probably best to upload elements individually then you can reuse them in other templates.